I want to have an task that occurs every week starting today. I click "new task". I enter title and start date. I set repeating to "every week" (the start date turns grey). So far so good. I can see that I have a planned task for 12th and 19th on a 7-day list. Cool.

Now I want to mark that I have finished the task on 12th. If I click empty box than both tasks - 12th and 19th - are marked as done. why ? I've marked only on of them... Is it possible to mark only the task at 12th as done ?

It's not directly an issue with recurring tasks. The issue is that the task list can't handle them and therefore is useless. If you enable the Tasks in View option in the View menu you'll see your recurring tasks in the main calendar view as long as they have a start and due date. If you edit the task from within the calendar view it will should work correctly.

There is a workaround for this issue. Just edit the single occurrence of the task.

I created a recurring task on Monday of every week. In Calendar view, right click on the Task on the Day of interest and Open it. Another box will open and select "Edit just this occurrence". Then change the Status to "Completed On". This marks just that occurrence as Completed. The subsequent occurrences of this task are still in the Calendar and not marked as complete.

If you want to see the completed tasks, go to View -> Current View and check "Show Completed Tasks"

I share this problem. If I mark a recurring task as completed, in the task summary the task is struck through. Tasks do not appear in the calendar so I'm unable to do the workaround referred to.

The only reference to the tasks in the calendar itself is that the date of the event is highlighted in the summary for the month but the task does not otherwise appear in the calendar. Does this make sense?

I did encounter a similar problem when using Korganizer where the solution was to show tasks as events.